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C7×C5⋊#10587716 #34062121

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊#10587716
unambiguous semidirect productC5⋊(C7×#10587716)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC5×C7×C13 ⋊ C2×C3×C7
HallC5×C7×#63270 ⋊ C2
HallC72×D65 ⋊ C3
HallC7×#63270 ⋊ D5
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ D13⋊C3
HallD65 ⋊ C7×ΓL(1,𝔽8)
HallC5×C13 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C5⋊(D13⋊C3)
SylowC13 ⋊ C7×D5×ΓL(1,𝔽8)
SylowC5 ⋊ C7×#10587716

Subgroups

subgroupG/H
center, hypercenterC7C5⋊#10587716
commutator, cosocle, hypocenterC5×C7×C13C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

630 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×#19129737, C7×#19129738, C7×#19129727, …
maximal normal subgroup ofC7×#19129737, C7×#19129738, C7×#19129727, …
maximal quotient ofC7×#19129697, C2×C7×C5⋊#10587716

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 114);